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Sum of Powers of 3

Source: AIME 2008II Problem 4

April 3, 2008
AMCAIME2008

Problem Statement

There exist r r unique nonnegative integers n1>n2>⋯>nr n_1 > n_2 > \cdots > n_r and r r unique integers ak a_k (1≤k≤r 1\le k\le r) with each ak a_k either 1 1 or \minus{} 1 such that a_13^{n_1} \plus{} a_23^{n_2} \plus{} \cdots \plus{} a_r3^{n_r} \equal{} 2008. Find n_1 \plus{} n_2 \plus{} \cdots \plus{} n_r.
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